Of course, the decline of science-as-an-institution isn't just marked by overt cheating. A safer and arguably more prevalent method is to game the publication system (ie by aligning your beliefs and professional contacts with powerful factions of reviewers), crank out many unrevealing publications, and make small contributions to hot fields rather than large ones in fields that are less likely to get you tenure.

Overall we'd see a lower signal-to-noise ratio in science, but this is hard to quantify. It's tough to call a discipline diseased until decades afterwards.